A particle moves along the x-axis with velocity given by v (t) = 3t2+6t for time tâ¥0. If the particle at position x=2 at time t=0, what is the position of the particle at time t=1?

a) 4

b) 6

c) 0

d) 11

e) 12

b) 6

Explanation:

Given

v (t) = 3t²+6t

X (0) = 2

X (1) = ?

Knowing that

v (t) = 3t²+6t = dX/dt

⇒ ∫dX = ∫ (3t²+6t) dt

⇒ X - X₀ = t³ + 3t²

⇒ X (t) = X₀ + t³ + 3t²

If X (0) = 2

⇒ X (0) = X₀ + (0) ³ + 3 (0) ² = 2

⇒ X₀ = 2

then we have

X (t) = t³ + 3t² + 2

when

t = 1

X (1) = (1) ³ + 3 (1) ² + 2

X (1) = 6

The answer is B) 6

Explanation:

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